Boyacı, Burak

Geroliminis, Nikolas

Kaspi, Mor

Repoux, Martin

Lancaster E-Prints

Predictive dynamic relocations in carsharingsystems implementing journey reservationsMartin REPOUXSchool of Architecture, Civil and Environmental Engineering (ENAC)E´cole Polytechnique Fe´de´rale de LausanneEmail: martin.repoux@epfl.chMor KASPIDepartment of Industrial EngineeringTel Aviv UniversityBurak BOYACILancaster University Management School (LUMS)Lancaster UniversityNikolas GEROLIMINISSchool of Architecture, Civil and Environmental Engineering (ENAC)E´cole Polytechnique Fe´de´rale de Lausanne1 IntroductionCarsharing is an on-demand shared-mobility service that aims at providing a level of servicesimilar to private vehicles while mutualizing the transportation resources. Several benefits linkedto its implementation have been identified both at user and society scale ([1, 2]). In this study,we focus on station-based carsharing systems which allow one-way rentals, namely vehicles canbe picked-up and dropped-off at different stations. In addition, the system imposes a reservationpolicy denoted as complete journey reservation policy, in which both a vehicle and a parking spothave to be reserved at the booking time. Reservations can be made up to one hour in advance andthe corresponding resources are kept reserved until the pick-up and drop-off times, respectively.Note that the exact times are not known to the system as users are not required to specify them inadvance. Such rental conditions are attractive to customers but they result in a less efficient use ofvehicles and spots due to extended reservation locking. In order to maximize resource availabilityin the system, the operator may introduce dynamic relocation schemes. Two main approachesexist in the literature: staff-based relocations, where car-sharing system employees move vehicles([3, 4, 5, 6, 7, 8, 9]) and user-based relocations, where customers adapt their trips according to theoperator’s suggestions ([10, 11]).This study presents a new proactive dynamic staff-based relocation algorithm tailored for thetype of systems considered, which aims at both reducing present imbalances in vehicle and spotavailability and preparing the system for the future demand. The algorithm is based on a Markovianmodel that incorporates reservation information and historical data in order to estimate the nearfuture expected demand loss at a station. Through a collaboration with the car-sharing system inGrenoble, France, we have conducted field experiments and extensive simulation experiments basedon data retrieved from the system. The outcome of the experiments demonstrate the superiorityof the proposed algorithm over other existing approaches.2 A Markovian estimation relocation policyWe apply a Markov chain based modeling approach to quantify the impact of relocation choiceson the expected demand loss due to shortages in vehicles or parking spots. This approach wasinitially proposed by [12], and was later adopted by several studies in the vehicle sharing literature.However, in this work we utilize for the first time reservation information in the model. Suchinformation is important especially for short term estimation periods as it reduces uncertaintyregarding vehicles and parking spots that are about to become available. On the one hand thisleads to a more complex model, on the other, it allows us to enhance near-future estimations.Consider a single station with C parking spots. Under the complete journey policy, the inven-tory state of each station can be described at any time by the triplet (xav, xrv, xrp), where xavis the number of available vehicles, xrv the number of reserved vehicles and xrp the number ofreserved spots. As capacity is fixed, the number of available parking spots is C − xav − xrv − xrp.The transitions between the inventory states of the station are due to four events: (i) reservationof an available vehicle with mean vehicle inter-reservation duration λ−1v , (ii) pick-up of a reservedvehicle with mean time between booking and pick-up µ−1v , (iii) drop-off of a vehicle with meantime between booking and drop-off µ−1p and (iv) reservation of an available spot with mean spotinter-reservation duration λ−1p . Transition rates out of state (xav, xrv, xrp) are detailed in Table 1.Event Current state Next state Transition rateBooking of available vehicle (xav , xrv , xrp) xav > 0 (xav − 1, xrv + 1, xrp) λv(t)Pick-up of booked vehicle (xav , xrv , xrp) (xav , xrv − 1, xrp) xrvµv(t)Drop-off of vehicle (xav , xrv , xrp) (xav + 1, xrv , xrp − 1) xrpµp(t)Booking of available spot (xav , xrv , xrp) xav + xrv + xrp < C (xav , xrv , xrp + 1) λp(t)Table 1: Transitions between states in the independent station Markov chain modelLet (xtav, xtrv, xtrp) be the state of the station at a decision time t, δ the estimation horizon andpixtav,xtrv,xtrpxav,xrv,xrs (τ) the probability that the station is in state (xav, xrv, xrs) at time τ , t ≥ τ ≥ t + δ.The expected demand loss due to vehicle and parking shortage at station s during δ is:ELst,δ(xtav, xtrv, xtrp) =∫ t+δt((C∑i=0C−i∑j=0pixtav,xtrv,xtrp0,i,j (τ))λv(τ) + (C∑i=0C−i∑j=0pixtav,xtrv,xtrpi,j,C−i−j (τ))λp(τ)dτThe first (resp.second) term in the integral represents the rate of requests that cannot be fulfilleddue to shortages in available vehicles (resp. spots), obtained by multiplying the probability forvehicle shortage (resp. spot shortage) at time τ by the arrival rate of requests for vehicles (resp.spots) λv(τ) (resp. λp(τ)). The evaluation of the expected demand loss is numerically obtainedwith the approximation method of [12]. In a single run of the procedure, expected demand lossesfor all stations, all initial states and the desired estimation horizon δ are obtained and stored tobe used later in the on-line relocation algorithm.The output of the model is applied in real-time decision making as described in the following. Inthe considered operation mode, relocators are required to reserve a vehicle and a spot as users do.If a station in state (xav, xrv, xrp) at decision time is selected as the origin of the next relocationtask assigned (and therefore has xav > 0), it transitions to state (xav − 1, xrv + 1, xrp) and theresulting avoided expected demand loss at this station is:Ost,δ(xav, xrv, xrp) = ELst,δ(xav, xrv, xrs)− ELst,δ(xav − 1, xrv + 1, xrp)Equivalently, if this station is the destination of the next relocation task assigned (and therefore issuch that xav +xrv +xrp < C), it transitions to state (xav, xrv, xrp+1) and the resulting expectedavoided demand loss is:Dst,δ(xav, xrv, xrp) = ELst,δ(xav, xrv, xrs)− ELst,δ(xav, xrv, xrp + 1)At a decision point, deciding to relocate a vehicle from station s1 to station s2 represents anexpected avoided demand loss of O+D. If O+D is negative for any pair of stations, no relocationis triggered. In selecting an origin-destination pair for a relocation task, we wish to balance theexpected avoided demand loss against the time required to execute the relocation task. In order todo so, we calculate the expected avoided demand loss per time unit spent relocating. Let move(s)be the time required for the relocator to move from his current location to station s, and letdrive(s1, s2) be the driving time from station s1 to station s2. The selected relocation pair (o?, d?)is the one with the highest positive expected avoided demand loss per time unit spent relocating:(o?, d?) = arg max(s1,s2)∈POs1t,δ(xs1av, xs1rv, xs1rp) +Ds2t,δ(xs2av, xs2rv, xs2rp)move(s1) + drive(s1, s2)Practically, the decision process is initiated any time a relocator completes a relocating task orwhen the state of the system is changed while some relocators are idle.3 Case study and resultsA collaboration with the car-sharing system in Grenoble has provided us unique opportunity totest our proposed algorithm in the field. In addition, we were able to base our simulation analysison trip transaction data obtained from the system. The Grenoble car-sharing system consisted of27 stations, each with 3 to 8 parking spots adding up to a total of 121 parking spots. The availablefleet size varied frequently between 40 to 55 vehicles, due to maintenance issues.In the experiments, we compared the Markovian estimation policy to the operators’ reloca-tion policy, to a no-relocation policy and to a purpose-built state of-the-art reactive inventoryrebalancing relocation policy (OVOS). The latter smartly combines the policies introduced in [4],namely inventory rebalancing and shortest-time relocations. In addition, we adapted a centralisticfull-knowledge relocation model [5] to generate an approximated upper bound on the performanceof the dynamic relocation policies.A three weeks field experiment conducted in June/October 2017, has shown that the OVOSand the Markovian estimation policy performed significantly better than the operator’s policy andthe no-relocation policy. In addition, it demonstrated the ability to implement of our policies in thefield and built knowledge to enhance the simulation framework. In the simulation experiment, weconsidered cases with 40, 60 and 80 vehicles in service. The daily demand levels investigated rangedbetween 100 and 400 and the staff size ranged between 1 to 3 relocators working simultaneously.For each demand level, 100 demand realizations consisting in 10 consecutive days of operation weredrawn from real data. The simulation results have shown that the Markovian policy served onaverage 1.3% to 4.5% more requests than the OVOS policy. As compared to the OVOS policy,which by itself resulted with high performance, the Markovian policy was able to close 10% to 30%of the gap to the approximated upper bound. As this bound is based on decision making usingfull information of the demand, the relative improvement is much higher than it seems.References[1] Richard Katzev. Car sharing: A new approach to urban transportation problems. Analysesof Social Issues and Public Policy, 3(1):65–86, 2003.[2] Michael Duncan. The cost saving potential of carsharing in a us context. Transportation,38(2):363–382, 2011.[3] Matthew Barth and Michael Todd. Simulation model performance analysis of a multiple sta-tion shared vehicle system. Transportation Research Part C: Emerging Technologies, 7(4):237–259, 1999.[4] Alvina GH Kek, Ruey Long Cheu, and Miaw Ling Chor. Relocation simulation model formultiple-station shared-use vehicle systems. Transportation research record, 1986(1):81–88,2006.[5] Burak Boyacı, Konstantinos G Zografos, and Nikolas Geroliminis. An integrated optimization-simulation framework for vehicle and personnel relocations of electric carsharing systems withreservations. Transportation Research Part B: Methodological, 95:214–237, 2017.[6] Claudio Gambella, Enrico Malaguti, Filippo Masini, and Daniele Vigo. Optimizing relocationoperations in electric car-sharing. Omega, 81:234–245, 2018.[7] Mehdi Nourinejad and Matthew J Roorda. A dynamic carsharing decision support system.Transportation research part E: logistics and transportation review, 66:36–50, 2014.[8] Rahul Nair and Elise Miller-Hooks. Fleet management for vehicle sharing operations. Trans-portation Science, 45(4):524–540, 2011.[9] Simone Weikl and Klaus Bogenberger. A practice-ready relocation model for free-floatingcarsharing systems with electric vehicles–mesoscopic approach and field trial results. Trans-portation Research Part C: Emerging Technologies, 57:206–223, 2015.[10] Matthew Barth, Michael Todd, and Lei Xue. User-based vehicle relocation techniques formultiple-station shared-use vehicle systems. 2004.[11] Angela Di Febbraro, Nicola Sacco, and Mahnam Saeednia. One-way car-sharing profit maxi-mization by means of user-based vehicle relocation. IEEE Transactions on Intelligent Trans-portation Systems, 2018.[12] Tal Raviv and Ofer Kolka. Optimal inventory management of a bike-sharing station. IIETransactions, 45(10):1077–1093, 2013.

Predictive dynamic relocations in carsharing systems implementing journey reservations

https://eprints.lancs.ac.uk/id/eprint/135602/1/repoux2019TSL.pdf

Predictive dynamic relocations in carsharing systems implementing journey reservations

Abstract

Similar works

Full text

Available Versions

Lancaster E-Prints